6.\\
$\begin{array} { l l l l l l l l l } 24 & 14 & 8 & x & 19 & 25 & 6 & 17 & 9 \end{array}$

The numbers in the list represent the exact weights, in kilograms, of 9 suitcases. One suitcase is weighed inaccurately and the only information known about the unknown weight, $x \mathrm {~kg}$, of this suitcase is that $19 < x \leqslant 23$. The suitcases are to be transported in containers that can hold a maximum of 50 kilograms.
\begin{enumerate}[label=(\alph*)]
\item Use the first-fit bin packing algorithm, on the list provided, to allocate the suitcases to containers.
\item Using the list provided, carry out a quick sort to produce a list of the weights in descending order. Show the result of each pass and identify your pivots clearly.
\item Apply the first-fit decreasing bin packing algorithm to the ordered list to determine the 2 possible allocations of suitcases to containers.

After the first-fit decreasing bin packing algorithm has been applied to the ordered list, one of the containers is full.
\item Calculate the possible integer values of $x$. You must show your working.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2014 Q6 [13]}}